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This paper proposes a new approach for the construction of highly secure physical unclonable functions (PUFs). Instead of using systems with medium information content and high readout rates, we suggest to maximize the information content of the PUF while strongly reducing its readout frequency. We show that special, passive crossbar arrays with a very large random information content and inherently limited readout speed are suited to implement our approach. They can conceal sensitive information over long time periods and can be made secure against invasive physical attacks. To support our feasibility study, circuit-level simulations and experimental data are presented. Our design allows the first PUFs that are secure against computationally unrestricted adversaries, and which remain so in the face of weeks or even years of uninterrupted adversarial access. We term the new design principle a “SHIC PUF,” where the acronym SHIC stands for super high information content.